Smooth sequence spaces and associated nuclearity

Terzioğlu, T.

doi:10.1090/S0002-9939-1973-0324372-5

Smooth sequence spaces and associated nuclearity
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Proc. Amer. Math. Soc. 37 (1973), 497-504 Request permission

Abstract:

We characterize $\lambda$-nuclear smooth sequence spaces where $\lambda$ itself is a smooth sequence space of infinite type. We also show that there is a duality between smooth sequence spaces of finite and infinite type.

References

B. S. Brudovskiĭ, Associated nuclear topology, type $s$ mappings and strongly nuclear spaces, Dokl. Akad. Nauk SSSR 178 (1968), 271–273 (Russian). MR 0226362
B. S. Brudovskiĭ, Type $s$ mappings of locally convex spaces, Dokl. Akad. Nauk SSSR 180 (1968), 15–17 (Russian). MR 0234243
Ed Dubinsky and M. S. Ramanujan, On $\lambda$-nuclearity, Memoirs of the American Mathematical Society, No. 128, American Mathematical Society, Providence, R.I., 1972. MR 0420215
Alexandre Grothendieck, Produits tensoriels topologiques et espaces nucléaires, Mem. Amer. Math. Soc. 16 (1955), Chapter 1: 196 pp.; Chapter 2: 140 (French). MR 75539
Gottfried Köthe, Über nukleare Folgenräume, Studia Math. 31 (1968), 267–271 (German). MR 236651, DOI 10.4064/sm-31-3-267-271
Gottfried Köthe, Stark nukleare Folgenräume, J. Fac. Sci. Univ. Tokyo Sect. I 17 (1970), 291–296 (German). MR 280970
Albrecht Pietsch, Nukleare lokalkonvexe Räume, Schriftenreihe Inst. Math. Deutsch. Akad. Wiss. Berlin, Reihe A, Reine Mathematik, Heft 1, Akademie-Verlag, Berlin, 1965 (German). MR 0181888
M. S. Ramanujan, Power series spaces $\Lambda (\alpha )$ and associated $\Lambda (\alpha )$-nuclearity, Math. Ann. 189 (1970), 161–168. MR 270110, DOI 10.1007/BF01352441
Tosun Terzioğlu, Die diametrale Dimension von lokalkonvexen Räumen, Collect. Math. 20 (1969), 49–99 (German). MR 253016
T. Terzioğlu, Nuclear and strongly nuclear sequence spaces, İstanbul Üniv. Fen Fak. Mecm. Ser. A 34 (1969), 1–5 (1971) (English, with Turkish summary). MR 305033